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Friction and Vertical Circular Motion Problems

A pendulum bo...

Question

A pendulum bob has a speed of $3 m s^{- 1}$ at its lowest position. The pendulum is $0.5 m$ long. What is the speed of the bob, when the length makes an angle of $60^{\circ}$ to the vertical? $(g = 10 m s^{- 2})$

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Solution

We know that,

$m v^{2} = m v_{1}^{2} + 2 m g h$

$9 = v_{1}^{2} + 2 (0.5 - 0.5 cos 60^{0}) \times 10$

$v_{1} = \sqrt{9 - 5}$

$v_{1} = 2 m / s$

Hence, the speed of the bob is $2 m / s$

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